Mrs May’s statement comes as the fifth round of negotiations began in Brussels. Focusing on technical issues, it is the final set of talks before EU leaders meet on 19 October to decide if enough progress has been made to talk about post-Brexit relations with the UK, including trade.

European Commission spokeswoman Margaritis Schinas said “the ball is entirely in the UK court” to reach agreement on Britain’s “divorce deal”, without which the EU has said it will not move on to the second phase of talks.

Mrs May appeared to reject that in her statement to MPs, saying: “As we look forward to the next stage, the ball is in their court.

“But I am optimistic we will receive a positive response.”

Mrs May also confirmed that the UK would remain subject to the rulings of the European Court of Justice during a planned two-year transition period after Britain leaves the EU in March 2019.

Responding to a challenge from Eurosceptic Conservative MP Jacob Rees-Mogg, she told MPs the need to ensure the minimum of disruption “may mean that we will start off with the ECJ still governing the rules we’re part of for that period”.

She said it was “highly unlikely” any new EU laws would come into force during the transition, but did not rule out the possibility that any which did so would have effect in Britain.

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Media captionJeremy Corbyn: “What on earth the government has been doing?”

The prime minister rejected existing models for economic co-operation, such as membership of the European Economic Area or the Canadian model, calling instead for a “creative” solution that would be “unique” to the UK.

But she also stressed – as she has done before – that the government was preparing for “every eventuality,” reinforcing her long-held position that walking away without a deal is a possibility.

She rejected a call from a Tory MP to name a date when the UK would walk away from talks without an agreement, saying “flexibility” was needed.

On Northern Ireland, she said the government had begun “drafting joint principles on preserving the Common Travel Area, and associated rights and we have both stated explicitly we will not accept any physical infrastructure at the border”.

The two White Papers give the most detail yet of contingency planning that is under way.

What’s in the White Papers?

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By Chris Morris, BBC Reality Check correspondent

The White Papers set out three strategic objectives: ensuring UK-EU trade is as frictionless as possible, avoiding a hard border between Ireland and Northern Ireland, and establishing the UK’s own independent international trade policy.

But there is also contingency planning, in case the UK leaves the EU without a negotiated settlement.

A customs bill will make provision for the UK to establish a stand-alone customs regime from day one, applying the same duties to every country with which it has no special deal.

The level of this duty would be set out in secondary legislation before the UK leaves the EU.

For high-volume roll-on roll-off ports, the legislation would require that consignments are pre-notified to customs authorities, to try to ensure that trade continues to flow as seamlessly as possible.

“No deal” is not the government’s preferred option; and the detail in the customs paper in particular hints at how disruptive it could be. But the UK wants the EU to know that it is planning for all eventualities.

Labour leader Jeremy Corbyn said the government had spent the 15 months since the EU referendum “squabbling amongst themselves” and were making a “mess” of Brexit.

He urged Mrs May to unilaterally guarantee the rights of EU citizens in the UK, as well as criticising the lack of progress on Northern Ireland.

The SNP’s leader at Westminster, Ian Blackford, said there had not been a single mention of the devolved administrations in Mrs May’s speech, as he called for urgent action on EU citizens’ rights.

The Liberal Democrats, who want a referendum on any final Brexit deal, urged the prime minister to “show real leadership” by ring-fencing the issue of EU citizens’ rights, confirming the UK will remain in the single market and customs union and firing Foreign Secretary Boris Johnson.

Jacob Rees-Mogg told the BBC he was “troubled” by the PM’s statement: “If we’re remaining under the jurisdiction of the ECJ then we haven’t left the European Union or the date of departure is being delayed.”

But Boris Johnson said the UK would “still be able to negotiate proper free trade deals” during the transition period.

“She (Theresa May) has reaffirmed the destination of a self-governing, free-trading, buccaneering and Global Britain taking back control over our laws, money, and borders,” he said in Facebook post.